BEHAVIOR OF SOLUTIONS OF BURGERS-EQUATION WITH NONLOCAL BOUNDARY-CONDITIONS

[摘要] In this paper, we discuss the long-time behavior of positive solutions of Burgers' equation u(t) = u(xx) + epsilonuu(x), 0 < x < 1, epsilon > 0, t > 0 with the nonlocal boundary condition: u(0, t) = 0, u(x)(1, t) + 1/2epsilonu2(1, t) = au(p)(1, t) (integral-0/1 u(x, t) dx)q, where 0 < p < infinity, 0 < q < infinity. Criteria for stability are given. Blowup in finite time for some solutions is shown. General results are discussed. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-15